Study Guide and Intervention (continued) - MathnMind

9-4
Solve Equations by Factoring Factoring and the Zero Product Property can be used
to solve some equations of the form ax 2 bx c 0.
Example
Solve 12x 2 3x 2 2x . Check your solutions.
12x2 3x 2 2x Original equation
12x2 5x 2 0 Rewrite equation so that one side equals 0.
(3x 2)(4x 1) 0 Factor the left side.
3x 2 0 or 4x1 0 Zero Product Property
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x 3
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x
4
Solve each equation.
2 1
The solution set is ,
3 4.
2 2
3 3
Since 12 2 3 2 2 and 12 2 3 2 2 , the solutions check.
Exercises
NAME ______________________________________________ DATE ____________ PERIOD _____
Study Guide and Intervention (continued)
Factoring Trinomials: ax 2 bx c
Solve each equation. Check your solutions.
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3
1. 8x 2 2x 3 0 2. 3n 2 2n 5 0 3. 2d 2 13d 7 0
4. 4x 2 x 3 5. 3x 2 13x 10 6. 6x 2 11x 10 0
7. 2k 2 40 11k 8. 2p 2 21p 40 9. 7 18x 9x 2 0
10. 12x 2 15 8x 11. 7a 2 65a 18 12. 16y 2 2y 3 0
13. 8x 2 5x 3 7x 14. 4a 2 18a 5 15 15. 3b 2 18b 10b 49
16. The difference of the squares of two consecutive odd integers is 24. Find the integers.
17. GEOMETRY The length of a Charlotte, North Carolina, conservatory garden is 20 yards
greater than its width. The area is 300 square yards. What are the dimensions?
18. GEOMETRY A rectangle with an area of 24 square inches is
formed by cutting strips of equal width from a rectangular piece
of paper. Find the dimensions of the new rectangle if the original
rectangle measures 8 inches by 6 inches.
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© Glencoe/McGraw-Hill 542 Glencoe Algebra 1
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